A single-polarization (SP) directional coupler based on dual-core photonic bandgap fiber (PBF) is proposed, and the coupling properties of the coupler are studied numerically using the full vector finite element method (FEM). Results show that by appropriately adjusting the size of the holes between the cores and the refractive index of doping, the SP property can be obtained in a coupler; however, the ellipticity of the hole between two cores has no effect on the SP property, which means that the coupler has high structure parameter error tolerance; an SP directional coupler with length of 0.403 mm is obtained by optimizing the parameters. In the application of the all polarization-maintaining PBF (PM-PBF) based resonant cavities, the coupler can serve as a beam splitter and a polarizer at the same time, break the resonant condition of secondary eigenstate of polarization (ESOP) and effectively inhibit its transmission. The mode field of SP coupler with short length matches with the PM-PBF proposed in former study, which is beneficial to the establishment of an all PM-PBF resonant cavities, and therefore has great significance in reducing the thermally induced polarization crosstalk noise of resonator fiber-optic gyroscopes (RFOG) and improving the long-term stability of RFOG.